In the field of deep learning, forward propagation, backpropagation and loss function are the three core concepts in building and training neural network models. Today, I will explain these three concepts and show how they work through a simple example.
Forward propagation: the "thinking" process of neural networks
Forward propagation is the foundational step in neural network computation, which involves passing the input data layer by layer through the weights and activation functions of the neural network, and ultimately outputting a prediction. This process involves"Sample Data Input, Algorithmic Model, Output."These are the steps.
Let's take a simple example. Let's show a picture to a little baby and ask him, "What is this picture?" He will use his little brain to "think" about the picture and then tell you the answer. Forward propagation is like this process, except that the baby is replaced by a neural network.
- Sample Data Input: This step converts sample data such as images, text, speech, etc. into numeric inputs that our computers can recognize. Just like a little baby sees a picture, the neural network also receives a picture and this picture is converted into a string of numbers.
- algorithmic modelIn simple terms, it is some mathematical calculations, mainly containing linear layer + regularization layer + activation, linear layer is responsible for doing the fitting of linear functions; regularization layer is responsible for regularizing our linear fitting, which is convenient for the later calculations; activation layer is responsible for becoming non-linear, because our real world is non-linear. So the whole process is: our input samples are nonlinear, and we go through a bunch of mathematical formulas like this to fit the nonlinear sample data.
- output layer: It is also some mathematical operations, such as Linear or Conv, which are responsible for converting the output of the model into a predictive result output.
This process can be represented by the following mathematical equation:
Loss function: telling the neural network how wrong it is
The loss function is a measure of the gap between the model's predictions and the true label, and its central role is to tell us how wrong the model's predictions are. In layman's terms.The loss function is like a referee who scores the model's predictions; the lower the score, the closer the model's predictions are to the real situation, and the better the model performs.. The loss function is there to allow us to backpropagate to work. Just like if a little baby guesses wrong, and you tell him, "Nope oh, it's the number 8, not 3," the loss function is like this sentence that tells the neural network, "Hey, your answer is a little off."
Here are a few commonly used loss functions:
L1 Loss（MAE）: Mean absolute error, more tolerant of outliers, but unable to proceed when the gradient drops to exactly 0. It's like when you tell your little baby, "How far off is your answer." That distance is the loss value.
L2 Loss（MSE）: Mean square error, continuous and smooth, easy to derive, but susceptible to outliers. It's like when you tell your little baby, "Your answer is off by how many units." The sum of the squares of this units is the loss value.
Smooth L1 Loss: Handling outliers is more robust, while avoiding the gradient explosion problem of L2 Loss. It's like when you tell your little baby, "How far off your answer was, but I'm not going to penalize you for guessing extraordinarily wrong." This loss function is more forgiving of extreme errors.
Backpropagation: the "self-correction" process of neural networks
Backpropagation is the process of updating the network parameters using the gradient of the loss function. It starts at the output layer and reverses through the network, using the chain rule to compute the gradient of each parameter with respect to the loss function. It contains these processes:
- Calculate the output layer error gradient: First calculate the error gradient of the output layer, which is the sensitivity of the loss function to the weights of the output layer.
- Layer-by-layer backpropagation: The error gradient is then computed layer by layer, starting at the output layer and working backwards through the network.
- Updating weights and biases: A gradient descent algorithm is used to update the weights and biases of each layer in the network based on the calculated gradients.
So the relationship between forward propagation, backpropagation, and loss function is this:
They are all central to the deep learning training process.forward propagationresponsible for generating forecasts.loss functionis responsible for quantifying the difference between the predicted outcome and the true label, while thebackward propagationis then responsible for using these differences to update the model parameters to reduce the value of the loss function.
By combining all three, we can build, train, and optimize deep learning models that can learn complex patterns from data and make accurate predictions in a variety of tasks such as image recognition, natural language processing, and predictive analytics.
Forward propagation, backpropagation, and loss function belong to the core concepts in the field of machine learning, and are the basis for understanding other more complex machine learning algorithms in the AI All Systems course. Mastering these concepts is important for learning machine learning in depth, understanding more advanced algorithms, and designing and optimizing models in real-world applications. By understanding forward propagation, backpropagation, and loss functions, learners are able to better grasp how machine learning models work, laying a solid foundation for further exploration of deep learning and other advanced machine learning techniques.